The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  X  X  X  X  0  X
 0  X  0  0  0  0  0  0 X^2 X^2  X  X  X  X X^2+X X^2 X^2+X  X  0
 0  0  X  0  0  0  0 X^2 X^2+X  X X^2+X  X X^2 X^2 X^2+X  0 X^2+X  0  X
 0  0  0  X  0  0  0 X^2+X X^2  X  X X^2+X X^2  0 X^2 X^2+X X^2+X X^2+X  0
 0  0  0  0  X  0  X  X X^2+X  0  X X^2  X X^2+X X^2  X X^2+X  0  X
 0  0  0  0  0  X  X X^2 X^2  X X^2+X X^2+X  0  0 X^2+X X^2 X^2+X  X  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+211x^12+718x^14+2201x^16+5008x^18+5102x^20+2300x^22+646x^24+160x^26+31x^28+6x^30

The gray image is a linear code over GF(2) with n=76, k=14 and d=24.
This code was found by Heurico 1.16 in 2.79 seconds.